On the Deuterium-to-Hydrogen Ratio of the Interstellar Medium

Observations show that the global deuterium-to-hydrogen ratio (D/H) in the local interstellar medium (ISM) is about 90% of the primordial ratio predicted by big bang nucleosynthesis. The high (D/H)$_{ISM}$ implies that only a small fraction of interstellar gas has been processed through stars, which destroy any deuterium they are born with. Using analytic arguments for one-zone chemical evolution models that include accretion and outflow, I show that the deuterium abundance is tightly coupled to the abundance of core collapse supernova (CCSN) elements such as oxygen. These models predict that the ratio of (D/H)$_{ISM}$ to the primordial abundance is $\approx 1/(1+r Z_O/m_O)$, where r is the recycling fraction, $Z_O$ is the ISM oxygen mass fraction, and $m_O$ is the population averaged CCSN yield of oxygen. Using values $r=0.4$ and $m_O=0.015$ appropriate to a Kroupa (2001) initial mass function and recent CCSN yield calculations, solar oxygen abundance corresponds to an ISM (D/H) that is 87\% of the primordial value, consistent with observations. This approximation is accurate for a wide range of parameter values, and physical arguments suggest that it should remain accurate for more complex chemical evolution models, making the deuterium abundance a robust prediction of almost any model that reproduces the observed ISM metallicity. The good agreement with the upper range of observed (D/H)$_{ISM}$ values supports the long-standing suggestion that sightline-to-sightline variations of deuterium are a consequence of dust depletion, rather than a low global (D/H)$_{ISM}$ enhanced by localized accretion of primordial composition gas. This agreement limits deviations from conventional yield and recycling values, and it implies that Galactic outflows eject ISM hydrogen as efficiently as they eject CCSN metals.